Solving Variational Problems Using Nonlinear Rotation-invariant Coordinates

Sassen, Josua; Heeren, Behrend; Hildebrandt, Klaus; Rumpf, Martin

Solving Variational Problems Using Nonlinear Rotation-invariant Coordinates

Files

001-002.pdf (6.4 MB)

Date

2019

Authors

Sassen, Josua
Heeren, Behrend
Hildebrandt, Klaus
Rumpf, Martin

Publisher

The Eurographics Association

Abstract

We consider Nonlinear Rotation-Invariant Coordinates (NRIC) representing triangle meshes with fixed combinatorics as a vector stacking all edge lengths and dihedral angles. Previously, conditions for the existence of vertex positions matching given NRIC have been established. We develop the machinery needed to use NRIC for solving geometric optimization problems. Moreover, we introduce a fast and robust algorithm that reconstructs vertex positions from close-to integrable NRIC. Our experiments underline that NRIC-based optimization is especially effective for near-isometric problems.

        @inproceedings{10.2312:sgp.20191213
,
booktitle = {Symposium on Geometry Processing 2019- Posters
},
editor = {Bommes, David and Huang, Hui
},
title = {{Solving Variational Problems Using Nonlinear Rotation-invariant Coordinates
}},
author = {Sassen, Josua and 
Heeren, Behrend and 
Hildebrandt, Klaus and 
Rumpf, Martin
},
year = {2019
},
publisher = {The Eurographics Association
},
ISSN = {1727-8384
},
ISBN = {978-3-03868-094-9
},
DOI = {10.2312/sgp.20191213
}
}